TSTP Solution File: REL002-1 by Geo-III---2018C
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- Process Solution
%------------------------------------------------------------------------------
% File : Geo-III---2018C
% Problem : REL002-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : geo -tptp_input -nonempty -inputfile %s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jul 23 06:14:36 EDT 2022
% Result : Unsatisfiable 2.14s 2.34s
% Output : Refutation 2.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : REL002-1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : geo -tptp_input -nonempty -inputfile %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Jul 23 00:37:04 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.14/2.34 GeoParameters:
% 2.14/2.34
% 2.14/2.34 tptp_input = 1
% 2.14/2.34 tptp_output = 0
% 2.14/2.34 nonempty = 1
% 2.14/2.34 inputfile = /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.14/2.34 includepath = /export/starexec/sandbox2/solver/bin/../../benchmark/
% 2.14/2.34
% 2.14/2.34
% 2.14/2.34 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.14/2.34 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.14/2.34
% 2.14/2.34 RuleSystem INPUT:
% 2.14/2.34
% 2.14/2.34 Initial Rules:
% 2.14/2.34 #0: input, references = 5, size of lhs = 3:
% 2.14/2.34 P_join-{F}(V0,V1,V2), P_join-{F}(V1,V0,V3), V2 == V3 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #1: input, references = 6, size of lhs = 5:
% 2.14/2.34 P_join-{F}(V1,V2,V3), P_join-{F}(V0,V3,V4), P_join-{F}(V0,V1,V5), P_join-{F}(V5,V2,V6), V4 == V6 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #2: input, references = 7, size of lhs = 8:
% 2.14/2.34 P_complement-{F}(V0,V2), P_complement-{F}(V1,V3), P_join-{F}(V2,V3,V4), P_complement-{F}(V4,V5), P_join-{F}(V2,V1,V6), P_complement-{F}(V6,V7), P_join-{F}(V5,V7,V8), V0 == V8 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #3: input, references = 7, size of lhs = 6:
% 2.14/2.34 P_meet-{F}(V0,V1,V2), P_complement-{F}(V0,V3), P_complement-{F}(V1,V4), P_join-{F}(V3,V4,V5), P_complement-{F}(V5,V6), V2 == V6 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #4: input, references = 3, size of lhs = 5:
% 2.14/2.34 P_composition-{F}(V1,V2,V3), P_composition-{F}(V0,V3,V4), P_composition-{F}(V0,V1,V5), P_composition-{F}(V5,V2,V6), V4 == V6 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #5: input, references = 4, size of lhs = 3:
% 2.14/2.34 P_one-{F}(V0), P_composition-{F}(V1,V0,V2), V2 == V1 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #6: input, references = 7, size of lhs = 7:
% 2.14/2.34 P_one-{F}(V0), P_join-{F}(V1,V2,V4), P_composition-{F}(V4,V3,V5), P_composition-{F}(V1,V3,V6), P_composition-{F}(V2,V3,V7), P_join-{F}(V6,V7,V8), V5 == V8 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #7: input, references = 4, size of lhs = 4:
% 2.14/2.34 P_one-{F}(V0), P_converse-{F}(V1,V2), P_converse-{F}(V2,V3), V3 == V1 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #8: input, references = 5, size of lhs = 7:
% 2.14/2.34 P_one-{F}(V0), P_join-{F}(V1,V2,V3), P_converse-{F}(V3,V4), P_converse-{F}(V1,V5), P_converse-{F}(V2,V6), P_join-{F}(V5,V6,V7), V4 == V7 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #9: input, references = 6, size of lhs = 7:
% 2.14/2.34 P_one-{F}(V0), P_composition-{F}(V1,V2,V3), P_converse-{F}(V3,V4), P_converse-{F}(V2,V5), P_converse-{F}(V1,V6), P_composition-{F}(V5,V6,V7), V4 == V7 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #10: input, references = 7, size of lhs = 8:
% 2.14/2.34 P_one-{F}(V0), P_converse-{F}(V1,V3), P_composition-{F}(V1,V2,V4), P_complement-{F}(V4,V5), P_composition-{F}(V3,V5,V6), P_complement-{F}(V2,V7), P_join-{F}(V6,V7,V8), V8 == V7 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #11: input, references = 6, size of lhs = 5:
% 2.14/2.34 P_one-{F}(V0), P_top-{F}(V1), P_complement-{F}(V2,V3), P_join-{F}(V2,V3,V4), V1 == V4 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #12: input, references = 4, size of lhs = 6:
% 2.14/2.34 P_one-{F}(V0), P_top-{F}(V1), P_zero-{F}(V2), P_complement-{F}(V3,V4), P_meet-{F}(V3,V4,V5), V2 == V5 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #13: input, references = 6, size of lhs = 5:
% 2.14/2.34 P_one-{F}(V0), P_top-{F}(V1), P_zero-{F}(V2), P_sk1-{F}(V3), P_join-{F}(V3,V1,V1) | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #14: input, references = 18, size of lhs = 2:
% 2.14/2.34 #-{F} V0, #-{F} V1 | EXISTS V2: P_join-{T}(V0,V1,V2)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #15: input, references = 10, size of lhs = 1:
% 2.14/2.34 #-{F} V0 | EXISTS V1: P_complement-{T}(V0,V1)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #16: input, references = 8, size of lhs = 2:
% 2.14/2.34 #-{F} V0, #-{F} V1 | EXISTS V2: P_meet-{T}(V0,V1,V2)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #17: input, references = 5, size of lhs = 2:
% 2.14/2.34 #-{F} V0, #-{F} V1 | EXISTS V2: P_composition-{T}(V0,V1,V2)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #18: input, references = 4, size of lhs = 0:
% 2.14/2.34 FALSE | EXISTS V0: P_one-{T}(V0)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #19: input, references = 15, size of lhs = 1:
% 2.14/2.34 #-{F} V0 | EXISTS V1: P_converse-{T}(V0,V1)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #20: input, references = 4, size of lhs = 0:
% 2.14/2.34 FALSE | EXISTS V0: P_top-{T}(V0)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #21: input, references = 4, size of lhs = 0:
% 2.14/2.34 FALSE | EXISTS V0: P_zero-{T}(V0)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #22: input, references = 4, size of lhs = 0:
% 2.14/2.34 FALSE | EXISTS V0: P_sk1-{T}(V0)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 number of initial rules = 23
% 2.14/2.34
% 2.14/2.34 Simplifiers:
% 2.14/2.34 #23: unsound, references = 3, size of lhs = 3:
% 2.14/2.34 P_join-{F}(V0,V1,V2), P_join-{F}(V0,V1,V5), V2 == V5 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #24: unsound, references = 3, size of lhs = 3:
% 2.14/2.34 P_complement-{F}(V0,V1), P_complement-{F}(V0,V3), V1 == V3 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #25: unsound, references = 3, size of lhs = 3:
% 2.14/2.34 P_meet-{F}(V0,V1,V2), P_meet-{F}(V0,V1,V5), V2 == V5 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #26: unsound, references = 3, size of lhs = 3:
% 2.14/2.34 P_composition-{F}(V0,V1,V2), P_composition-{F}(V0,V1,V5), V2 == V5 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #27: unsound, references = 3, size of lhs = 3:
% 2.14/2.34 P_one-{F}(V0), P_one-{F}(V1), V0 == V1 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #28: unsound, references = 3, size of lhs = 3:
% 2.14/2.34 P_converse-{F}(V0,V1), P_converse-{F}(V0,V3), V1 == V3 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #29: unsound, references = 3, size of lhs = 3:
% 2.14/2.34 P_top-{F}(V0), P_top-{F}(V1), V0 == V1 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #30: unsound, references = 3, size of lhs = 3:
% 2.14/2.34 P_zero-{F}(V0), P_zero-{F}(V1), V0 == V1 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #31: unsound, references = 3, size of lhs = 3:
% 2.14/2.34 P_sk1-{F}(V0), P_sk1-{F}(V1), V0 == V1 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 number of simplifiers = 9
% 2.14/2.34
% 2.14/2.34 Learnt:
% 2.14/2.34 #33: exists( #14, #11 ), references = 13, size of lhs = 3:
% 2.14/2.34 P_one-{F}(V0), P_top-{F}(V1), P_complement-{F}(V2,V3) | P_join-{T}(V2,V3,V1)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #37: exists( #15, #3 ), references = 16, size of lhs = 4:
% 2.14/2.34 P_complement-{F}(V0,V1), P_meet-{F}(V0,V2,V3), P_complement-{F}(V2,V4), P_join-{F}(V1,V4,V5) | P_complement-{T}(V5,V3)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #43: exists( #16, #12 ), references = 3, size of lhs = 4:
% 2.14/2.34 P_one-{F}(V0), P_top-{F}(V1), P_zero-{F}(V2), P_complement-{F}(V3,V4) | P_meet-{T}(V3,V4,V2)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #55: exists( #19, #9 ), references = 1, size of lhs = 5:
% 2.14/2.34 P_one-{F}(V0), P_converse-{F}(V1,V2), P_composition-{F}(V3,V1,V4), P_converse-{F}(V3,V5), P_composition-{F}(V2,V5,V6) | P_converse-{T}(V4,V6)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #57: exists( #14, #0 ), references = 27, size of lhs = 1:
% 2.14/2.34 P_join-{F}(V0,V1,V2) | P_join-{T}(V1,V0,V2)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #60: exists( #19, #8 ), references = 5, size of lhs = 5:
% 2.14/2.34 P_one-{F}(V0), P_converse-{F}(V1,V2), P_join-{F}(V1,V3,V4), P_converse-{F}(V3,V5), P_join-{F}(V2,V5,V6) | P_converse-{T}(V4,V6)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #64: exists( #14, #1 ), references = 27, size of lhs = 3:
% 2.14/2.34 P_join-{F}(V0,V1,V2), P_join-{F}(V3,V0,V4), P_join-{F}(V4,V1,V5) | P_join-{T}(V3,V2,V5)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #70: exists( #17, #5 ), references = 14, size of lhs = 2:
% 2.14/2.34 P_one-{F}(V0), #-{F} V1 | P_composition-{T}(V1,V0,V1)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #75: exists( #19, #7 ), references = 10, size of lhs = 2:
% 2.14/2.34 P_one-{F}(V0), P_converse-{F}(V1,V2) | P_converse-{T}(V2,V1)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #85: exists( #14, #82 ), references = 2, size of lhs = 11:
% 2.14/2.34 P_complement-{F}(V0,V1), P_complement-{F}(V2,V1), P_join-{F}(V1,V3,V4), P_join-{F}(V3,V5,V6), P_complement-{F}(V7,V6), P_meet-{F}(V0,V7,V8), P_complement-{F}(V9,V6), P_join-{F}(V1,V9,V10), P_complement-{F}(V10,V11), P_join-{F}(V8,V11,V12), V2 == V12 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #95: exists( #14, #93 ), references = 1, size of lhs = 12:
% 2.14/2.34 P_one-{F}(V0), P_top-{F}(V1), P_zero-{F}(V2), P_complement-{F}(V3,V4), P_join-{F}(V4,V5,V6), P_join-{F}(V5,V7,V8), P_complement-{F}(V9,V8), P_meet-{F}(V3,V9,V10), P_complement-{F}(V10,V11), P_join-{F}(V10,V11,V12), P_complement-{F}(V12,V13), V2 == V13 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #97: exists( #15, #94 ), references = 1, size of lhs = 10:
% 2.14/2.34 P_one-{F}(V0), P_top-{F}(V1), P_zero-{F}(V2), P_complement-{F}(V3,V4), P_join-{F}(V4,V5,V6), P_join-{F}(V5,V7,V8), P_complement-{F}(V9,V8), P_meet-{F}(V3,V9,V10), P_complement-{F}(V10,V11), P_join-{F}(V10,V11,V12) | P_complement-{T}(V12,V2)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #104: exists( #14, #102 ), references = 1, size of lhs = 11:
% 2.14/2.34 P_complement-{F}(V0,V1), P_complement-{F}(V2,V1), P_join-{F}(V1,V3,V4), P_join-{F}(V3,V5,V6), P_complement-{F}(V7,V6), P_meet-{F}(V0,V7,V8), P_complement-{F}(V9,V6), P_join-{F}(V1,V9,V10), P_complement-{F}(V10,V11), P_join-{F}(V12,V13,V11), P_join-{F}(V8,V12,V14) | P_join-{T}(V13,V14,V2)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #124: exists( #17, #9 ), references = 14, size of lhs = 5:
% 2.14/2.34 P_one-{F}(V0), P_converse-{F}(V1,V2), P_composition-{F}(V3,V1,V4), P_converse-{F}(V4,V5), P_converse-{F}(V3,V6) | P_composition-{T}(V2,V6,V5)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #133: exists( #14, #131 ), references = 1, size of lhs = 8:
% 2.14/2.34 P_one-{F}(V0), P_converse-{F}(V1,V2), P_composition-{F}(V1,V3,V4), P_complement-{F}(V4,V5), P_composition-{F}(V2,V5,V6), P_complement-{F}(V3,V7), P_join-{F}(V8,V9,V7), P_join-{F}(V6,V8,V10) | P_join-{T}(V9,V10,V7)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #153: mergings( V3 == V5, V4 == V6; #148 ), references = 1, size of lhs = 9:
% 2.14/2.34 P_one-{F}(V0), P_top-{F}(V1), P_complement-{F}(V2,V3), P_complement-{F}(V4,V5), P_join-{F}(V3,V5,V6), P_complement-{F}(V7,V6), P_meet-{F}(V7,V6,V8), P_join-{F}(V1,V8,V9), V1 == V9 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #154: exists( #16, #146 ), references = 2, size of lhs = 12:
% 2.14/2.34 P_one-{F}(V0), P_top-{F}(V1), P_join-{F}(V2,V1,V1), P_complement-{F}(V3,V2), P_join-{F}(V2,V4,V1), P_join-{F}(V4,V4,V5), V3 == V5, P_complement-{F}(V6,V7), P_complement-{F}(V8,V9), P_join-{F}(V7,V9,V10), P_complement-{F}(V11,V10), P_meet-{F}(V11,V10,V4) | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #156: mergings( V3 == V5; #150 ), references = 1, size of lhs = 12:
% 2.14/2.34 P_top-{F}(V0), P_one-{F}(V1), P_composition-{F}(V2,V0,V0), P_converse-{F}(V2,V3), P_complement-{F}(V4,V5), P_complement-{F}(V6,V7), P_join-{F}(V5,V7,V8), P_complement-{F}(V9,V8), P_meet-{F}(V9,V8,V10), P_composition-{F}(V3,V10,V11), P_join-{F}(V11,V10,V12), V12 == V10 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #201: mergings( V2 == V4, V3 == V5; #198 ), references = 1, size of lhs = 6:
% 2.14/2.34 P_one-{F}(V0), P_top-{F}(V1), P_zero-{F}(V2), P_complement-{F}(V1,V3), V2 == V3, P_complement-{F}(V4,V5) | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #205: mergings( V2 == V3, V0 == V4; #202 ), references = 1, size of lhs = 3:
% 2.14/2.34 P_one-{F}(V0), P_top-{F}(V1), P_zero-{F}(V2) | P_complement-{T}(V1,V2)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #207: exists( #14, #10 ), references = 4, size of lhs = 6:
% 2.14/2.34 P_one-{F}(V0), P_converse-{F}(V1,V2), P_composition-{F}(V1,V3,V4), P_complement-{F}(V4,V5), P_composition-{F}(V2,V5,V6), P_complement-{F}(V3,V7) | P_join-{T}(V6,V7,V7)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #213: exists( #16, #3 ), references = 1, size of lhs = 4:
% 2.14/2.34 P_complement-{F}(V0,V1), P_complement-{F}(V2,V3), P_join-{F}(V1,V3,V4), P_complement-{F}(V4,V5) | P_meet-{T}(V0,V2,V5)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #226: mergings( V0 == V2, V2 == V3; #223 ), references = 1, size of lhs = 1:
% 2.14/2.34 P_one-{F}(V0) | P_converse-{T}(V0,V0)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #229: exists( #14, #6 ), references = 3, size of lhs = 5:
% 2.14/2.34 P_one-{F}(V0), P_join-{F}(V1,V2,V3), P_composition-{F}(V3,V4,V5), P_composition-{F}(V1,V4,V6), P_composition-{F}(V2,V4,V7) | P_join-{T}(V6,V7,V5)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #259: mergings( V7 == V9, V14 == V15, V2 == V3, V3 == V4, V4 == V5; #252 ), references = 1, size of lhs = 11:
% 2.14/2.34 P_one-{F}(V0), P_converse-{F}(V0,V1), P_join-{F}(V1,V1,V1), P_complement-{F}(V2,V2), P_join-{F}(V3,V4,V2), P_complement-{F}(V5,V6), P_join-{F}(V6,V3,V7), P_join-{F}(V7,V2,V8), P_complement-{F}(V8,V9), P_join-{F}(V9,V9,V10), V5 == V10 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #265: mergings( V7 == V11, V2 == V3, V3 == V4, V4 == V5, V5 == V6; #253 ), references = 1, size of lhs = 15:
% 2.14/2.34 P_one-{F}(V0), P_top-{F}(V1), P_join-{F}(V1,V1,V2), P_converse-{F}(V0,V3), P_join-{F}(V3,V3,V3), P_join-{F}(V4,V1,V1), P_join-{F}(V5,V6,V1), P_join-{F}(V7,V5,V4), P_complement-{F}(V8,V7), V8 == V2, P_complement-{F}(V9,V10), P_complement-{F}(V11,V12), P_join-{F}(V10,V12,V13), P_complement-{F}(V14,V13), P_meet-{F}(V14,V13,V1) | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #277: mergings( V10 == V11, V2 == V4, V4 == V5, V5 == V6, V6 == V7; #270 ), references = 1, size of lhs = 10:
% 2.14/2.34 P_top-{F}(V0), P_complement-{F}(V0,V0), P_one-{F}(V1), P_converse-{F}(V1,V2), P_join-{F}(V2,V2,V2), P_join-{F}(V0,V0,V3), P_complement-{F}(V3,V4), P_join-{F}(V4,V4,V5), #-{F} V6, V6 == V5 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #284: mergings( V8 == V9, V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V7; #271 ), references = 1, size of lhs = 12:
% 2.14/2.34 P_one-{F}(V0), P_top-{F}(V1), P_join-{F}(V1,V1,V1), P_converse-{F}(V0,V2), P_join-{F}(V2,V2,V2), P_complement-{F}(V3,V4), P_complement-{F}(V5,V6), P_join-{F}(V4,V6,V7), P_complement-{F}(V8,V7), P_meet-{F}(V8,V7,V1), #-{F} V9, V9 == V1 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #293: exists( #16, #291 ), references = 2, size of lhs = 9:
% 2.14/2.34 P_one-{F}(V0), P_top-{F}(V1), P_complement-{F}(V1,V2), P_join-{F}(V2,V2,V2), P_complement-{F}(V3,V2), V3 == V1, P_complement-{F}(V4,V5), P_join-{F}(V5,V6,V2), P_complement-{F}(V7,V6) | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #312: mergings( V8 == V10, V2 == V3, V3 == V4, V4 == V5; #307 ), references = 1, size of lhs = 7:
% 2.14/2.34 P_one-{F}(V0), P_converse-{F}(V0,V1), P_converse-{F}(V1,V2), P_complement-{F}(V3,V4), P_composition-{F}(V2,V4,V5), P_join-{F}(V5,V4,V6), V6 == V4 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #341: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6; #334 ), references = 2, size of lhs = 12:
% 2.14/2.34 P_one-{F}(V0), P_top-{F}(V1), P_complement-{F}(V1,V2), P_complement-{F}(V3,V2), P_complement-{F}(V4,V2), V4 == V1, P_complement-{F}(V5,V2), P_complement-{F}(V6,V2), P_converse-{F}(V0,V7), P_converse-{F}(V8,V7), P_composition-{F}(V8,V3,V9), P_complement-{F}(V9,V2) | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #366: mergings( V7 == V12, V2 == V3, V3 == V4, V4 == V5, V5 == V6; #360 ), references = 1, size of lhs = 8:
% 2.14/2.34 P_one-{F}(V0), P_top-{F}(V1), P_zero-{F}(V2), P_sk1-{F}(V3), P_converse-{F}(V0,V4), P_converse-{F}(V4,V5), P_composition-{F}(V5,V1,V3), P_complement-{F}(V6,V1) | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #371: exists( #14, #8 ), references = 4, size of lhs = 5:
% 2.14/2.34 P_one-{F}(V0), P_converse-{F}(V1,V2), P_join-{F}(V1,V3,V4), P_converse-{F}(V4,V5), P_converse-{F}(V3,V6) | P_join-{T}(V2,V6,V5)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #409: mergings( V2 == V3, V3 == V4, V4 == V5; #403 ), references = 3, size of lhs = 10:
% 2.14/2.34 P_one-{F}(V0), P_converse-{F}(V0,V1), P_converse-{F}(V2,V1), P_composition-{F}(V2,V3,V4), P_complement-{F}(V4,V5), P_complement-{F}(V3,V6), P_join-{F}(V7,V6,V8), P_join-{F}(V7,V5,V9), P_join-{F}(V9,V6,V10), V8 == V10 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #416: mergings( V3 == V4, V4 == V5, V5 == V6; #412 ), references = 10, size of lhs = 10:
% 2.14/2.34 P_one-{F}(V0), P_converse-{F}(V0,V1), P_converse-{F}(V2,V1), P_composition-{F}(V2,V3,V4), P_complement-{F}(V4,V5), P_complement-{F}(V3,V6), P_join-{F}(V6,V7,V8), P_join-{F}(V7,V9,V10), P_join-{F}(V11,V5,V10), P_join-{F}(V11,V6,V12) | P_join-{T}(V8,V9,V12)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #445: exists( #14, #441 ), references = 1, size of lhs = 8:
% 2.14/2.34 P_one-{F}(V0), P_top-{F}(V1), P_complement-{F}(V2,V3), P_join-{F}(V3,V4,V5), P_join-{F}(V6,V5,V5), P_meet-{F}(V2,V7,V6), P_complement-{F}(V7,V8), P_join-{F}(V4,V9,V8) | P_join-{T}(V9,V5,V1)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #446: exists( #14, #442 ), references = 1, size of lhs = 15:
% 2.14/2.34 P_one-{F}(V0), P_top-{F}(V1), P_complement-{F}(V1,V2), P_complement-{F}(V3,V2), P_complement-{F}(V4,V2), P_complement-{F}(V5,V2), P_converse-{F}(V0,V6), P_converse-{F}(V7,V6), P_composition-{F}(V7,V3,V8), P_complement-{F}(V8,V2), P_complement-{F}(V9,V10), P_meet-{F}(V9,V11,V2), P_complement-{F}(V11,V12), P_join-{F}(V13,V14,V12), P_join-{F}(V10,V13,V15) | P_join-{T}(V14,V15,V1)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #489: mergings( V3 == V4, V4 == V5, V5 == V6, V6 == V7, V7 == V8, V9 == V11; #482 ), references = 1, size of lhs = 18:
% 2.14/2.34 P_one-{F}(V0), P_converse-{F}(V1,V1), P_converse-{F}(V0,V2), P_converse-{F}(V2,V2), P_converse-{F}(V3,V3), P_converse-{F}(V4,V5), P_converse-{F}(V6,V5), P_join-{F}(V7,V6,V3), P_join-{F}(V1,V7,V8), P_converse-{F}(V8,V9), P_join-{F}(V4,V6,V10), P_join-{F}(V10,V8,V11), P_converse-{F}(V11,V12), P_complement-{F}(V13,V14), P_meet-{F}(V13,V15,V5), P_complement-{F}(V15,V16), P_join-{F}(V17,V6,V16), P_join-{F}(V14,V17,V8) | P_join-{T}(V6,V8,V12)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #559: mergings( V3 == V4, V4 == V7, V7 == V8, V8 == V9, V9 == V11, V5 == V12, V12 == V13; #549 ), references = 1, size of lhs = 22:
% 2.14/2.34 P_top-{F}(V0), P_converse-{F}(V0,V0), P_one-{F}(V1), P_converse-{F}(V1,V2), P_converse-{F}(V2,V2), P_converse-{F}(V3,V2), P_converse-{F}(V4,V4), P_complement-{F}(V5,V6), P_join-{F}(V6,V7,V4), P_composition-{F}(V3,V5,V8), P_complement-{F}(V8,V9), P_join-{F}(V10,V6,V0), P_join-{F}(V10,V9,V11), P_join-{F}(V7,V12,V13), P_join-{F}(V14,V12,V0), P_join-{F}(V4,V14,V15), P_join-{F}(V13,V15,V11), P_complement-{F}(V16,V17), P_join-{F}(V17,V18,V15), P_join-{F}(V18,V12,V19), P_complement-{F}(V20,V19), P_meet-{F}(V16,V20,V21) | P_join-{T}(V12,V15,V0)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #567: mergings( V3 == V4, V4 == V7, V7 == V8, V8 == V9, V9 == V11, V5 == V12, V12 == V13; #550 ), references = 1, size of lhs = 24:
% 2.14/2.34 P_top-{F}(V0), P_converse-{F}(V0,V0), P_one-{F}(V1), P_converse-{F}(V1,V2), P_converse-{F}(V2,V2), P_converse-{F}(V3,V2), P_converse-{F}(V4,V4), P_composition-{F}(V3,V5,V6), P_complement-{F}(V6,V7), P_complement-{F}(V5,V8), P_join-{F}(V9,V8,V0), P_join-{F}(V9,V7,V10), P_join-{F}(V8,V11,V12), P_join-{F}(V12,V13,V4), P_join-{F}(V0,V13,V14), P_join-{F}(V11,V15,V16), P_join-{F}(V17,V15,V4), P_join-{F}(V0,V17,V18), P_join-{F}(V16,V18,V10), P_complement-{F}(V19,V20), P_join-{F}(V20,V21,V18), P_join-{F}(V21,V15,V22), P_complement-{F}(V23,V22), P_meet-{F}(V19,V23,V24) | P_join-{T}(V15,V18,V14)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #577: mergings( V15 == V17, V3 == V4, V4 == V7, V7 == V8, V8 == V9, V9 == V11, V11 == V13, V5 == V12, V12 == V14; #551 ), references = 1, size of lhs = 24:
% 2.14/2.34 P_top-{F}(V0), P_one-{F}(V1), P_converse-{F}(V1,V2), P_converse-{F}(V2,V2), P_converse-{F}(V3,V2), P_converse-{F}(V4,V4), P_composition-{F}(V0,V5,V4), P_converse-{F}(V6,V6), P_composition-{F}(V7,V5,V6), P_complement-{F}(V8,V9), P_join-{F}(V9,V10,V7), P_composition-{F}(V3,V8,V11), P_complement-{F}(V11,V12), P_join-{F}(V13,V9,V0), P_join-{F}(V13,V12,V14), P_join-{F}(V10,V15,V16), P_join-{F}(V17,V15,V6), P_join-{F}(V4,V17,V18), P_join-{F}(V16,V18,V14), P_complement-{F}(V19,V20), P_join-{F}(V20,V21,V18), P_join-{F}(V21,V15,V22), P_complement-{F}(V23,V22), P_meet-{F}(V19,V23,V24) | P_join-{T}(V15,V18,V4)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #594: mergings( V3 == V4, V4 == V7, V7 == V8, V8 == V9, V9 == V11, V11 == V14, V14 == V17, V5 == V12, V12 == V13, V13 == V15; #582 ), references = 1, size of lhs = 33:
% 2.14/2.34 P_top-{F}(V0), P_converse-{F}(V0,V0), P_one-{F}(V1), P_converse-{F}(V1,V2), P_converse-{F}(V2,V2), P_converse-{F}(V3,V2), P_converse-{F}(V4,V2), P_converse-{F}(V5,V5), P_complement-{F}(V6,V7), P_join-{F}(V7,V8,V5), P_composition-{F}(V3,V6,V9), P_complement-{F}(V9,V10), P_join-{F}(V11,V7,V0), P_join-{F}(V11,V10,V12), P_join-{F}(V8,V13,V14), P_join-{F}(V15,V13,V0), P_join-{F}(V5,V15,V16), P_join-{F}(V14,V16,V12), P_complement-{F}(V17,V18), P_join-{F}(V18,V19,V16), P_join-{F}(V19,V13,V20), P_complement-{F}(V21,V20), P_composition-{F}(V4,V22,V23), P_complement-{F}(V23,V24), P_complement-{F}(V22,V25), P_join-{F}(V25,V13,V26), P_join-{F}(V27,V24,V0), P_join-{F}(V27,V25,V28), P_composition-{F}(V28,V29,V30), P_composition-{F}(V26,V29,V31), P_composition-{F}(V16,V29,V32), P_join-{F}(V31,V32,V33), V30 == V33 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #606: mergings( V3 == V4, V4 == V7, V7 == V8, V8 == V9, V9 == V11, V11 == V14, V14 == V17, V5 == V12, V12 == V13, V13 == V15, V10 == V18; #583 ), references = 1, size of lhs = 30:
% 2.14/2.34 P_one-{F}(V0), P_converse-{F}(V0,V1), P_converse-{F}(V1,V1), P_converse-{F}(V2,V1), P_converse-{F}(V3,V1), P_top-{F}(V4), P_converse-{F}(V4,V4), P_zero-{F}(V5), P_sk1-{F}(V6), P_converse-{F}(V7,V7), P_join-{F}(V7,V8,V4), P_join-{F}(V8,V9,V4), P_join-{F}(V10,V9,V6), P_complement-{F}(V11,V10), P_composition-{F}(V3,V11,V12), P_complement-{F}(V12,V13), P_join-{F}(V14,V13,V4), P_join-{F}(V14,V10,V4), P_complement-{F}(V15,V16), P_join-{F}(V16,V17,V7), P_composition-{F}(V2,V15,V18), P_complement-{F}(V18,V19), P_join-{F}(V20,V16,V4), P_join-{F}(V20,V19,V21), P_join-{F}(V17,V9,V22), P_join-{F}(V22,V4,V21), P_complement-{F}(V23,V24), P_join-{F}(V24,V25,V4), P_join-{F}(V25,V9,V26), P_complement-{F}(V27,V26) | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #623: mergings( V8 == V9, V11 == V12, V2 == V3, V3 == V4, V4 == V5, V6 == V7; #616 ), references = 2, size of lhs = 7:
% 2.14/2.34 P_one-{F}(V0), P_converse-{F}(V0,V1), P_converse-{F}(V1,V1), P_complement-{F}(V2,V3), P_join-{F}(V4,V3,V5), P_join-{F}(V5,V3,V6), V5 == V6 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #631: mergings( V2 == V4; #629 ), references = 1, size of lhs = 7:
% 2.14/2.34 P_top-{F}(V0), P_one-{F}(V1), P_converse-{F}(V1,V2), P_converse-{F}(V2,V2), P_join-{F}(V3,V4,V0), P_join-{F}(V0,V4,V5), V0 == V5 | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #636: mergings( V3 == V5; #634 ), references = 2, size of lhs = 7:
% 2.14/2.34 P_top-{F}(V0), P_one-{F}(V1), P_converse-{F}(V1,V2), P_converse-{F}(V2,V2), P_join-{F}(V0,V3,V4), P_join-{F}(V3,V5,V6), P_join-{F}(V7,V6,V0) | P_join-{T}(V5,V4,V0)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #645: mergings( V2 == V3, V3 == V4; #642 ), references = 1, size of lhs = 6:
% 2.14/2.34 P_one-{F}(V0), P_join-{F}(V1,V1,V1), P_converse-{F}(V2,V1), P_composition-{F}(V3,V2,V3), P_join-{F}(V3,V3,V4), P_converse-{F}(V4,V5) | P_converse-{T}(V3,V5)
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #671: mergings( V15 == V16, V18 == V10, V2 == V3, V3 == V4, V4 == V5, V5 == V7, V7 == V9, V6 == V8, V8 == V14; #661 ), references = 1, size of lhs = 11:
% 2.14/2.34 P_one-{F}(V0), P_top-{F}(V1), P_zero-{F}(V2), P_sk1-{F}(V3), P_join-{F}(V4,V3,V1), P_converse-{F}(V0,V5), P_converse-{F}(V5,V5), P_join-{F}(V6,V4,V1), P_join-{F}(V7,V6,V1), P_complement-{F}(V8,V7), P_join-{F}(V9,V7,V1) | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #683: mergings( V2 == V3, V3 == V4, V4 == V5, V5 == V6, V6 == V8, V8 == V10, V7 == V9, V9 == V13; #674 ), references = 1, size of lhs = 6:
% 2.14/2.34 P_one-{F}(V0), P_top-{F}(V1), P_zero-{F}(V2), P_sk1-{F}(V3), P_converse-{F}(V0,V4), P_converse-{F}(V4,V4) | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #693: mergings( V1 == V2, V2 == V3, V3 == V4, V4 == V5, V5 == V7, V7 == V9, V6 == V8, V8 == V12; #684 ), references = 1, size of lhs = 5:
% 2.14/2.34 P_one-{F}(V0), P_top-{F}(V1), P_zero-{F}(V2), P_converse-{F}(V0,V3), P_converse-{F}(V3,V3) | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #703: mergings( V1 == V2, V2 == V3, V3 == V4, V4 == V5, V5 == V7, V7 == V9, V6 == V8, V8 == V11; #694 ), references = 1, size of lhs = 4:
% 2.14/2.34 P_one-{F}(V0), P_top-{F}(V1), P_converse-{F}(V0,V2), P_converse-{F}(V2,V2) | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #713: mergings( V1 == V2, V2 == V3, V3 == V4, V4 == V5, V5 == V7, V7 == V9, V6 == V8, V8 == V10; #704 ), references = 1, size of lhs = 3:
% 2.14/2.34 P_one-{F}(V0), P_converse-{F}(V0,V1), P_converse-{F}(V1,V1) | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 #716: exists( #18, #714 ), references = 1, size of lhs = 0:
% 2.14/2.34 FALSE | FALSE
% 2.14/2.34 (used 0 times, uses = {})
% 2.14/2.34
% 2.14/2.34 number of learnt formulas = 53
% 2.14/2.34
% 2.14/2.34
% 2.14/2.34 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.14/2.34
% 2.14/2.34 randbase = 1
%------------------------------------------------------------------------------